372 lines
10 KiB
Nim
372 lines
10 KiB
Nim
# Constantine
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# Copyright (c) 2018-2019 Status Research & Development GmbH
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# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
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# Licensed and distributed under either of
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# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
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# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
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# at your option. This file may not be copied, modified, or distributed except according to those terms.
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import std/unittest,
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../../constantine/math/arithmetic,
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../../constantine/math/arithmetic/limbs_montgomery,
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../../constantine/math/io/[io_bigints, io_fields],
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../../constantine/math/config/curves
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static: doAssert defined(testingCurves), "This modules requires the -d:testingCurves compile option"
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echo "\n------------------------------------------------------\n"
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proc main() =
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suite "Basic arithmetic over finite fields":
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test "Addition mod 101":
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block:
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var x, y, z: Fp[Fake101]
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x.fromUint(80'u32)
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y.fromUint(10'u32)
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z.fromUint(90'u32)
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x += y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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90'u64 == cast[uint64](x_bytes)
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block:
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var x, y, z: Fp[Fake101]
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x.fromUint(80'u32)
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y.fromUint(21'u32)
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z.fromUint(0'u32)
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x += y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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0'u64 == cast[uint64](x_bytes)
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block:
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var x, y, z: Fp[Fake101]
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x.fromUint(80'u32)
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y.fromUint(22'u32)
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z.fromUint(1'u32)
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x += y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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1'u64 == cast[uint64](x_bytes)
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test "Substraction mod 101":
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block:
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var x, y, z: Fp[Fake101]
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x.fromUint(80'u32)
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y.fromUint(10'u32)
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z.fromUint(70'u32)
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x -= y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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70'u64 == cast[uint64](x_bytes)
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block:
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var x, y, z: Fp[Fake101]
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x.fromUint(80'u32)
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y.fromUint(80'u32)
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z.fromUint(0'u32)
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x -= y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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0'u64 == cast[uint64](x_bytes)
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block:
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var x, y, z: Fp[Fake101]
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x.fromUint(80'u32)
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y.fromUint(81'u32)
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z.fromUint(100'u32)
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x -= y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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100'u64 == cast[uint64](x_bytes)
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test "Multiplication mod 101":
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block:
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var x, y, z, r: Fp[Fake101]
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x.fromUint(10'u32)
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y.fromUint(10'u32)
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z.fromUint(100'u32)
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r.prod(x, y)
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var r_bytes: array[8, byte]
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r_bytes.exportRawUint(r, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == r)
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# Check equality when converting back to natural domain
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100'u64 == cast[uint64](r_bytes)
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block:
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var x, y, z, r: Fp[Fake101]
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x.fromUint(10'u32)
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y.fromUint(11'u32)
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z.fromUint(9'u32)
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r.prod(x, y)
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var r_bytes: array[8, byte]
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r_bytes.exportRawUint(r, cpuEndian)
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check:
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# Check equality in the Montgomery domain
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bool(z == r)
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# Check equality when converting back to natural domain
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9'u64 == cast[uint64](r_bytes)
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test "Addition mod 2^61 - 1":
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block:
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var x, y, z: Fp[Mersenne61]
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x.fromUint(80'u64)
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y.fromUint(10'u64)
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z.fromUint(90'u64)
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x += y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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let new_x = cast[uint64](x_bytes)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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new_x == 90'u64
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block:
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var x, y, z: Fp[Mersenne61]
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x.fromUint(1'u64 shl 61 - 2)
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y.fromUint(1'u32)
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z.fromUint(0'u32)
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x += y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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let new_x = cast[uint64](x_bytes)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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new_x == 0'u64
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block:
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var x, y, z: Fp[Mersenne61]
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x.fromUint(1'u64 shl 61 - 2)
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y.fromUint(2'u64)
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z.fromUint(1'u64)
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x += y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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let new_x = cast[uint64](x_bytes)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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new_x == 1'u64
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test "Substraction mod 2^61 - 1":
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block:
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var x, y, z: Fp[Mersenne61]
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x.fromUint(80'u64)
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y.fromUint(10'u64)
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z.fromUint(70'u64)
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x -= y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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let new_x = cast[uint64](x_bytes)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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new_x == 70'u64
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block:
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var x, y, z: Fp[Mersenne61]
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x.fromUint(0'u64)
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y.fromUint(1'u64)
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z.fromUint(1'u64 shl 61 - 2)
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x -= y
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var x_bytes: array[8, byte]
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x_bytes.exportRawUint(x, cpuEndian)
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let new_x = cast[uint64](x_bytes)
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check:
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# Check equality in the Montgomery domain
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bool(z == x)
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# Check equality when converting back to natural domain
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new_x == 1'u64 shl 61 - 2
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test "Multiplication mod 2^61 - 1":
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block:
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var x, y, z, r: Fp[Mersenne61]
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x.fromUint(10'u32)
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y.fromUint(10'u32)
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z.fromUint(100'u32)
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r.prod(x, y)
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var r_bytes: array[8, byte]
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r_bytes.exportRawUint(r, cpuEndian)
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let new_r = cast[uint64](r_bytes)
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check:
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# Check equality in the Montgomery domain
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bool(z == r)
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# Check equality when converting back to natural domain
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cast[uint64](r_bytes) == 100'u64
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block:
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var x, y, z, r: Fp[Mersenne61]
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x.fromUint(1'u32 shl 31)
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y.fromUint(1'u32 shl 31)
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z.fromUint(2'u32)
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r.prod(x, y)
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var r_bytes: array[8, byte]
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r_bytes.exportRawUint(r, cpuEndian)
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let new_r = cast[uint64](r_bytes)
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check:
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# Check equality in the Montgomery domain
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bool(z == r)
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# Check equality when converting back to natural domain
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new_r == 2'u64
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main()
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proc largeField() =
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suite "Large field":
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test "Negate 0 returns 0 (unique Montgomery repr)":
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# https://github.com/mratsim/constantine/issues/136
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# and https://github.com/mratsim/constantine/issues/114
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# The assembly implementation of neg didn't check
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# after M-a if a was zero and so while in mod M
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# M ≡ 0 (mod M), the `==` doesn't support unreduced representation.
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var a: Fp[BN254_Snarks]
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var r {.noInit.}: Fp[BN254_Snarks]
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r.neg(a)
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check: bool r.isZero()
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test "fromMont doesn't need a final substraction with 256-bit prime (full word used)":
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block:
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var a: Fp[Secp256k1]
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a.mres = Fp[Secp256k1].getMontyPrimeMinus1()
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let expected = BigInt[256].fromHex"0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2E"
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var r: BigInt[256]
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r.fromField(a)
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check: bool(r == expected)
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block:
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var a: Fp[Secp256k1]
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var d: FpDbl[Secp256k1]
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# Set Montgomery repr to the largest field element in Montgomery Residue form
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a.mres = BigInt[256].fromHex"0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2E"
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d.limbs2x = (BigInt[512].fromHex"0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2E").limbs
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var r, expected: BigInt[256]
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r.fromField(a)
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expected.limbs.redc2xMont(d.limbs2x, Secp256k1.Mod().limbs, Fp[Secp256k1].getNegInvModWord(), Fp[Secp256k1].getSpareBits())
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check: bool(r == expected)
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test "fromMont doesn't need a final substraction with 255-bit prime (1 spare bit)":
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block:
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var a: Fp[Edwards25519]
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a.mres = Fp[Edwards25519].getMontyPrimeMinus1()
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let expected = BigInt[255].fromHex"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec"
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var r: BigInt[255]
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r.fromField(a)
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check: bool(r == expected)
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block:
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var a: Fp[Edwards25519]
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var d: FpDbl[Edwards25519]
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# Set Montgomery repr to the largest field element in Montgomery Residue form
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a.mres = BigInt[255].fromHex"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec"
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d.limbs2x = (BigInt[512].fromHex"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec").limbs
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var r, expected: BigInt[255]
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r.fromField(a)
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expected.limbs.redc2xMont(d.limbs2x, Edwards25519.Mod().limbs, Fp[Edwards25519].getNegInvModWord(), Fp[Edwards25519].getSpareBits())
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check: bool(r == expected)
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largeField()
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